Title: Operated Algebras and Derived Structures
Speaker: Prof. Li Guo
Affiliation: Rutgers University-Newark, USA
Time: June 27-28, 2025 (10:10-11:10 & 14:00-15:00 daily)
Location: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
While most algebraic studies have traditionally focused on structures with binary or higher-arity operations, algebras equipped with linear operators have historically emerged from various mathematical applications. However, systematic algebraic investigations of such structures have been limited, primarily concentrating on specific instances like differential algebras and Rota-Baxter algebras. The recent introduction of operated algebras as a general framework has shown promising developments.
This lecture series will present recent advances in the general theory of operated algebras, their important classes, and derived structures, covering the following aspects:
Fundamental concepts of operated semigroups and algebras, including combinatorial constructions of free objects
Key examples of operated algebras and Rota's classification program
Algebraic approaches to integral operators and equations through operated algebras
Derived structures in operadic contexts
Multi-operated algebras and compatible structures, particularly multi-Rota-Baxter, multi-pre-Lie, multi-differential, and multi-Novikov algebras
Speaker's Biography:
Prof. Li Guo of Rutgers University-Newark is a distinguished mathematician whose number theory contributions were cited in Wiles' proof of Fermat's Last Theorem. He pioneered the application of renormalization methods from physics to mathematical research. Recently, he has been leading advancements in Rota-Baxter algebras and related mathematical physics, authoring the field's first comprehensive monograph and presenting the subject in the AMS "What Is..." series.
His extensive research spans:
Associative algebras, Lie algebras, and Hopf algebras
Operad theory and combinatorics
Computational mathematics and number theory
Quantum field theory and integrable systems
